All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=16.4cm,clip]{0191f01.eps} \end{figure}$ Figure 1: K-band mosaic of the Galactic centre cluster obtained in March 2007; coordinates are RA and Dec in arcsec relative to Sgr A*. This image covers a FOV of $\approx$ 1.5 $\times$ 1.5 pc. The contrast was enhanced by applying unsharp masking. The position of Sgr A* is marked with a cross in the image centre. The dotted line crossing the image indicates the Galactic plane. Stars with names are SiO maser stars used for defining an astrometric reference frame.
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In the text

$\begin{figure} \par\includegraphics[trim = 0cm 0cm 1cm 0cm, clip, height=7.3cm,a... ...f02b.eps}\par\includegraphics[height=7.3cm,angle=-90]{0191f02c.eps} \end{figure}$ Figure 2: Residual image alignment errors before and after distortion correction and image registration, comparing the overlap area (right hand half of the first image of the data set) of two 27 mas/pixel scale K band images obtained in March 2007. Arrows mark absolute values (1 unit = 2 milli-pixels) and directions of residuals, $\delta x$ ( $\delta y$ ) are the rms of residuals in x (y). Top panel: sub-pixel accurate shift-and-add only. Central panel: after correcting for geometric distortion, before registration. Bottom panel: after distortion correction and registration.
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In the text

$\begin{figure} \par\mbox{\includegraphics[height=8.6cm, angle=-90]{0191f03a.eps}\hspace{3mm} \includegraphics[height=8.6cm,angle=-90]{0191f03b.eps} }\end{figure}$ Figure 3: Statistical uncertainty of absolute radio reference frame coordinates as a function of position due to transformation errors, separately for RA ( left hand panel) and Dec ( right hand panel). The contour values are given in units of milli-arcseconds. Across the field of view the errors vary in the range 1.2 ... 5 mas. The contours mirror the alignment of the reference stars in the sky plane (see Fig. 1).
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In the text

$\begin{figure} \par\includegraphics[trim = 0cm 0cm 0.9cm 0cm, clip, height=8.8cm... ...f04a.eps}\par\includegraphics[height=8.8cm,angle=-90]{0191f04b.eps} \end{figure}$ Figure 4: Histograms of proper motion errors. Top panel: large pixel scale (27 mas/pix). Bottom panel: small pixel scale (13 mas/yr). The distributions peak at $\approx$ 0.18 mas/yr in case of the large pixel scale and at $\approx$ 0.1 mas/yr in case of the small pixel scale, corresponding to 6.8 km s^-1 and 3.8 km s^-1 respectively.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f05.eps} \end{figure}$ Figure 5: Histogram of statistical errors in line-of-sight velocity for 664 stars. The distribution peaks at $\approx$ 7 km s^-1.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f06.eps} \end{figure}$ Figure 6: K magnitude distributions of all 5445 (non early-type) proper motion stars (black curve) and the 664 3D velocity stars (grey curve). Please note the different binnings. The distributions peak in the range $K\approx 15...16$ ; this is the regime of the Red Clump stars. For K>16, the completeness quickly decreases.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f07.eps} \end{figure}$ Figure 7: Modulations in stellar proper motions. Shown here is the number of stars vs. angle of the proper motion vectors. The angle is defined as atan2(v_x, v_y) and counted from north to east. Black points with error bars are the data; horizontal error bars mark the full bin widths, vertical error bars are Poisson $\sqrt {N}$ errors. This diagram tests the preferential orientations of proper motion vectors on sky. The vertical dashed grey lines mark the location of the Galactic plane (+27.1 $^{\circ }$ and counter-direction). A cosine fit to the data (grey curve) finds a phase $\phi$ = +30 $\pm$ $5^{\circ }$ , in agreement with the orientation of the Galaxy.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f08a.eps}\par\includegraphics[height=8.8cm,angle=-90]{0191f08b.eps} \end{figure}$ Figure 8: Signatures of rotation and/or anisotropy in proper motions and radial velocities. Top panel: angle on sky (counted from N to E) vs. difference in square dispersions $\Delta \sigma ^2 = \sigma _{\parallel }^2 - \sigma _{\perp }^2$ . Here $\sigma _{\parallel }$ ( $\sigma _{\perp }$ ) is the velocity dispersion parallel (perpendicular) to a given principal axis which is rotated stepwise. The black dots and the black curve show the observed modulation, dashed black curves mark the 1- $\sigma$ uncertainty range. Vertical grey dashed lines mark the position of the Galactic plane, the horizontal grey dashed line is the zero level of $\Delta \sigma ^2$ . The modulation has an amplitude of $\Delta \sigma _{\rm max}^2=2.00$ $\pm$ 0.21 (mas/yr)². Bottom panel: average radial velocities $\langle {v}_z\rangle$ vs. Galactic longitude l. Black points are the data, error bars along the l axis mark the full bin sizes, error bars in velocity direction are 1- $\sigma$ -errors. Grey dashed lines mark the zero levels of l and $\langle {v}_z\rangle$ . As the number of stars is smaller for l<0, errors are larger in this range. A linear fit to the data (continuous black line) obtains a rotation velocity of 1.4 $\pm$ 0.4 km s^-1/arcsec.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f09.eps} \end{figure}$ Figure 9: Histograms of proper motions in l and b of all proper motion stars. Error bars mark the Poisson errors. Dotted lines represent the respective best-fitting Gaussians. Average velocities $\langle {v}_{l, b}\rangle$ and velocity dispersions $\sigma _{l, b}$ are given in the plot. Whereas the b velocities appear to be normally distributed, the l velocities show a clear rotation pattern.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f10.eps} \end{figure}$ Figure 10: Distribution of stellar speeds for all 3D velocity stars. Points with error bars are data; errors in star numbers are Poisson errors, errors in v mark the full bin widths. The continuous grey line corresponds to a superposition of Maxwellian distributions for local velocity dispersions $\sigma _{\rm 3D}(r)$ ; this line is not a fit to the data. Observed and model distributions are in good agreement; we find $\chi ^2_{\rm red}=1.16$ .
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f11a.eps}\par\includegraphics[height=8.8cm,angle=-90]{0191f11b.eps} \end{figure}$ Figure 11: Velocity dispersion profiles. Top panel: proper motion dispersions. Squares with error bars are observed velocity dispersions $\sigma _{l, b}$ vs. projected distance from Sgr A* r. Continuous lines mark the best-fitting cluster model assuming a spherical, rotating system (please see the text for details). Bottom panel: observed radial velocity dispersions. As the number of 3D velocity stars is about nine times smaller than the number of 2D velocity stars, the profile is sampled sparsely compared to the proper motion dispersion profile.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f12.eps} \end{figure}$ Figure 12: Average radial velocity vs. Galactic longitude l as derived from our modelling (continuous grey line). For comparison, the observed values (black data points with error bars) are given. The data are from our work and from McGinn et al. (1989).
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f13.eps} \end{figure}$ Figure 13: Stellar surface mass density $\Sigma$ vs. projected distance r from Sgr A* for the model cluster.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f14.eps} \end{figure}$ Figure 14: Enclosed mass vs. distance from Sgr A* calculated via the Jeans equation for 1''<R<100''. The continuous black curve is the mass profile using our best-fitting model density profile with break radius R_b=8.9''. The continuous grey line shows the profile obtained when neglecting the flattening of the density profile towards small R, i.e. assuming R_b=0. The corresponding dashed curves are the stellar mass profiles obtained by subtracting the central point masses (i.e. the values found at R=0). The scale is 1 pc $\equiv$ 25.8''.
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In the text

$\begin{figure} \par\mbox{\includegraphics[height=8.5cm,angle=-90]{0191f15a.eps}\... ...pace{3mm} \includegraphics[height=8.5cm,angle=-90]{0191f15f.eps} }\end{figure}$ Figure 15: Velocity-coordinate phase-space maps. Velocities in the sky plane v_l,b include all 5445 proper motion stars; line-of-sight velocities v_z are given for 664 stars. The scale is 1 mas/yr $\equiv$ 37.9 km s^-1. Compared to the v_b, the v_l distributions are broadened (in velocity) due to the global rotation. The v_z are biased towards positive l as SINFONI spectra were collected mainly north of Sgr A*. These global properties aside, the diagrams show no obvious patterns or sub-structures.
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In the text

$\begin{figure} \par\mbox{\includegraphics[height=8cm,angle=-90]{0191f16a.eps}\hs... ...hspace{5mm} \includegraphics[height=8cm,angle=-90]{0191f16d.eps} }\end{figure}$ Figure 16: Velocity-velocity phase-space maps. The distribution of v_l vs. v_b is given twice, once for all 5445 proper motion stars ( top left) in mas/yr, once for all 664 3D motion stars ( top right) in km s^-1. The scale is 1 mas/yr $\equiv$ 37.9 km s^-1. In analogy to Fig. 15, the global rotation shows up as a broadening of the v_l,z distributions with respect to v_b (see also Figs. 9, 18). These global properties aside, there is no obvious substructure or grouping.
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In the text

$\begin{figure} \par\mbox{\includegraphics[height=8.7cm,angle=-90]{0191f17a.eps}\hspace{3mm} \includegraphics[height=8.7cm,angle=-90]{0191f17b.eps} }\end{figure}$ Figure 17: 4D two-point correlation functions for all proper motion stars. The normalized distance s is defined via $s^2=(\Delta l/x_0)^2 + (\Delta b/x_0)^2 + (\Delta {v}_l/v_0)^2 + (\Delta {v}_b/v_0)^2$ ; x₀, v₀ are constants. Please note the different $\xi (s)$ axis scales. Left hand panel: measured phase-space distances compared to a uniform random distribution. The profile mirrors the obvious clustering of phase-space points around (l,b,v_l,v_b)=(0,0,0,0) shown in Figs. 15, 16. Right hand panel: measured phase-space distances compared to a Monte-Carlo model of the GC cluster. Deviations from the uniform rotator model cluster do not exceed $\approx$ 0.04.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f18a.eps}\par\includegraphics[height=8.8cm,angle=-90]{0191f18b.eps} \end{figure}$ Figure 18: Histograms of proper motions in l and b ( top panel) and of radial velocities ( bottom panel) including all stars with measured 3D velocities. The dotted curve in the bottom panel corresponds to the best-fitting Gaussian profile. Error bars mark the Poisson errors. In both plots the respective average velocities $\langle {v}_{l, b, z}\rangle$ and velocity dispersions $\sigma _{l, b, z}$ are given.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f19.eps} \end{figure}$ Figure 19: Acceleration upper limits (99% confidence level) vs. projected distance r from Sgr A*. Dots mark measured values. The continuous line corresponds to the acceleration a star would experience if its physical distance from Sgr A* would equal its projected distance. The distance scale is 1 pc $\equiv$ 25.8''. This sample includes 750 of 755 analysed stars. Stars below the line have a physical distance that is necessarily larger than the projected distance.
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In the text

$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f20a.eps}\vspace{3mm} \par\includegraphics[height=8.8cm,angle=-90]{0191f20b.eps} \end{figure}$ Figure 20: Proper motion maps for the IRS13E group. Filled circles are stars, circle diameters are proportional to the 0.25th power of H-band fluxes. Coordinates are $\alpha$ , $\delta$ in arcsec relative to Sgr A*; please note the shift in $\alpha$ . Arrows are proper motions, 1 unit in length corresponds to 10 mas/yr. Boxes around arrow heads indicate the 1- $\sigma$ velocity uncertainties. Top panel: proper motions co-moving with the GC cluster as defined in Sect. 3. Bottom panel: proper motions co-moving with the central three brightest stars. A streaming motion of the three brightest stars relative to a foreground/background population can be seen. Apparently, only a small fraction, if any, of the examined stars are bound to the IRS13E group.
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In the text

$\begin{figure} \par\includegraphics[trim = 0cm 0cm 0.9cm 0cm, clip, height=8.8cm... ...f04a.eps}\par\includegraphics[height=8.8cm,angle=-90]{0191f04b.eps} \end{figure}$	Figure 4: Histograms of proper motion errors. Top panel: large pixel scale (27 mas/pix). Bottom panel: small pixel scale (13 mas/yr). The distributions peak at $\approx$ 0.18 mas/yr in case of the large pixel scale and at $\approx$ 0.1 mas/yr in case of the small pixel scale, corresponding to 6.8 km s^-1 and 3.8 km s^-1 respectively.
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$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f05.eps} \end{figure}$	Figure 5: Histogram of statistical errors in line-of-sight velocity for 664 stars. The distribution peaks at $\approx$ 7 km s^-1.
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$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f06.eps} \end{figure}$	Figure 6: K magnitude distributions of all 5445 (non early-type) proper motion stars (black curve) and the 664 3D velocity stars (grey curve). Please note the different binnings. The distributions peak in the range $K\approx 15...16$ ; this is the regime of the Red Clump stars. For K>16, the completeness quickly decreases.
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$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f09.eps} \end{figure}$	Figure 9: Histograms of proper motions in l and b of all proper motion stars. Error bars mark the Poisson errors. Dotted lines represent the respective best-fitting Gaussians. Average velocities $\langle {v}_{l, b}\rangle$ and velocity dispersions $\sigma _{l, b}$ are given in the plot. Whereas the b velocities appear to be normally distributed, the l velocities show a clear rotation pattern.
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$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f12.eps} \end{figure}$	Figure 12: Average radial velocity vs. Galactic longitude l as derived from our modelling (continuous grey line). For comparison, the observed values (black data points with error bars) are given. The data are from our work and from McGinn et al. (1989).
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$\begin{figure} \par\includegraphics[height=8.8cm,angle=-90]{0191f13.eps} \end{figure}$	Figure 13: Stellar surface mass density $\Sigma$ vs. projected distance r from Sgr A* for the model cluster.
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